Subtracting two rational expressions with unlike denominators

Learn how to add/subtract rational expressions with trinomials in the denominator. When adding or subtracting two or more rational expressions with common denominators, we add or subtract only the numerator while we keep the denominator the same. We will then simplify our answer by reducing the fraction if necessary.

When adding rational expressions with different denominators, we first factor the denominators (if possible), before finding the LCM of the different denominators (this is usually the product of the different expressions that makes up the denominators). We then multiply the denominators by an expression which will yield the LCM. You will also multiply the numerator by the same expression with which you multiplied the denominator.

Notice that the expressions now have the same denominator. We can now add or subtract the numerators while retaining the common denominator.

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